An ideal gas expands isothermally and reversibly from $10 \mathrm{~m}^{3}$ to $20 \mathrm{~m}^{3}$ at $300…

An ideal gas expands isothermally and reversibly from $10 \mathrm{~m}^{3}$ to $20 \mathrm{~m}^{3}$ at $300 \mathrm{~K}$, performing $5 \cdot 187 \mathrm{~kJ}$ of work on surrounding, calculate number of moles of gas used?
  1. 1
  2. 3
  3. 2
  4. 1.5

Solution

$\begin{array}{l} V_{1}=10 \mathrm{~m}^{3}=10 \times 10^{3} \mathrm{dm}^{3} \\ V_{2}=20 \mathrm{~m}^{3}=20 \times 10^{3} \mathrm{dm}^{3} \end{array}$ $T=300 K, W=-5.187 \mathrm{~kJ}=-5187 \mathrm{~J}$ $W=-2.303 \mathrm{nRT} \log \frac{V_{2}}{V_{1}}$ $\therefore-5187=-2.303 \times n \times 8.314 \times 300 \times \log _{10} \frac{20 \times 10^{3}}{10 \times 10^{3}}$ $\therefore n=\frac{5187}{2.303 \times 8.314 \times 300 \times 0.301}$ $\therefore n=3$ moles

Asked in: MHT CET 2020 (16 Oct Shift 1)

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